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Simplifying -7(t + -4) + 3(6t + 7) = 10(t + 7) + -9 Reorder the terms: -7(-4 + t) + 3(6t + 7) = 10(t + 7) + -9 (-4 * -7 + t * -7) + 3(6t + 7) = 10(t + 7) + -9 (28 + -7t) + 3(6t + 7) = 10(t + 7) + -9 Reorder the terms: 28 + -7t + 3(7 + 6t) = 10(t + 7) + -9 28 + -7t + (7 * 3 + 6t * 3) = 10(t + 7) + -9 28 + -7t + (21 + 18t) = 10(t + 7) + -9 Reorder the terms: 28 + 21 + -7t + 18t = 10(t + 7) + -9 Combine like terms: 28 + 21 = 49 49 + -7t + 18t = 10(t + 7) + -9 Combine like terms: -7t + 18t = 11t 49 + 11t = 10(t + 7) + -9 Reorder the terms: 49 + 11t = 10(7 + t) + -9 49 + 11t = (7 * 10 + t * 10) + -9 49 + 11t = (70 + 10t) + -9 Reorder the terms: 49 + 11t = 70 + -9 + 10t Combine like terms: 70 + -9 = 61 49 + 11t = 61 + 10t Solving 49 + 11t = 61 + 10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10t' to each side of the equation. 49 + 11t + -10t = 61 + 10t + -10t Combine like terms: 11t + -10t = 1t 49 + 1t = 61 + 10t + -10t Combine like terms: 10t + -10t = 0 49 + 1t = 61 + 0 49 + 1t = 61 Add '-49' to each side of the equation. 49 + -49 + 1t = 61 + -49 Combine like terms: 49 + -49 = 0 0 + 1t = 61 + -49 1t = 61 + -49 Combine like terms: 61 + -49 = 12 1t = 12 Divide each side by '1'. t = 12 Simplifying t = 12
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